Ideal Gas Law Calculator

1. Enter any three of pressure, volume, amount and temperature.
2. Use kelvin for temperature (add 273.15 to Celsius).
3. Leave the one you want to find blank.
4. Read the result and the formula used.

Here is what each result means:

The ideal gas law links the four properties that describe a gas: its pressure, its volume, how much of it there is, and its temperature. In one compact equation, pressure times volume equals the number of moles times the gas constant times the absolute temperature. Know any three and the fourth is fixed.

The gas constant R ties the units together and equals 8.314 joules per mole per kelvin in SI units. The law treats gas particles as tiny, non-interacting points, which is an idealisation, but real gases follow it closely at everyday pressures and temperatures. It is one of the most useful relationships in all of chemistry and physics.

A key requirement is that temperature must be absolute, measured in kelvin, not Celsius. That is because the law is built on the idea that a gas would have zero pressure and volume at absolute zero. Forgetting to convert Celsius to kelvin is the most common source of wrong answers, so always add 273.15 to a Celsius temperature first.

It rearranges the ideal gas law to solve for whichever value you leave blank.

1. For pressure, multiply moles, R and temperature, then divide by volume.
2. For volume, multiply moles, R and temperature, then divide by pressure.
3. For amount, multiply pressure by volume, then divide by R times temperature.
4. For temperature, multiply pressure by volume, then divide by moles times R.

Gases store energy and exert pressure; see the pressure calculator and molarity calculator.

Find the pressure of 1 mole of gas at 273.15 kelvin in 0.0224 cubic meters.

Calculation: P = (1 x 8.314 x 273.15) / 0.0224, which is about 101,325 pascals, or one atmosphere. This is the standard molar volume of a gas at 0 degrees Celsius.

One law, rearranged for whatever you need to find.

All four come from PV equals nRT, so any three of the values give the fourth. Because R is a fixed constant, the law effectively links just the four measurable properties of the gas, which is why it appears in almost every gas problem in chemistry.

The ideal gas law combines three older laws that each hold one thing constant.

Each simple law is a special case of PV equals nRT with two quantities fixed. The ideal gas law is more powerful because it handles all four properties at once, so you rarely need the individual laws when you have this calculator.

The Temperature Scale

Temperature must be in kelvin. Using Celsius gives a badly wrong answer, especially near room temperature.

The Units

With R = 8.314, use pascals, cubic meters, moles and kelvin. Mixed units break the result.

Real-gas Behaviour

At very high pressure or very low temperature, real gases deviate from the ideal law.

Chemistry Homework

Solve for pressure, volume, moles or temperature in a gas problem.

Laboratory Work

Predict how a gas responds when conditions change.

Engineering

Estimate gas behaviour in tanks, engines and processes.

1. Using Celsius

Temperature must be in kelvin. Add 273.15 to a Celsius value before entering it.

2. Wrong Units

With R = 8.314, use pascals, cubic meters and moles. Liters and atmospheres need a different R.

3. Volume in Liters

Convert liters to cubic meters by dividing by 1000, since one liter is 0.001 cubic meters.

4. Forgetting R

The gas constant links the units. It is built into the calculator as 8.314.

5. Applying It to Extremes

The ideal gas law is least accurate at very high pressure or very low temperature.

The relation is exact for an ideal gas; only the displayed decimals are rounded, and very large or small results are shown in scientific notation.

The ideal gas law states that pressure times volume equals moles times the gas constant times absolute temperature, written PV = nRT. It links the four main properties of a gas in one equation.

Multiply the moles, the gas constant and the temperature in kelvin, then divide by the volume. For 1 mole at 273.15 kelvin in 0.0224 cubic meters, the pressure is about 101,325 pascals.

The gas constant R is 8.314 joules per mole per kelvin in SI units. If you work in liters and atmospheres, R is instead 0.0821 liter atmospheres per mole per kelvin.

The law assumes a gas would reach zero pressure and volume at absolute zero. Kelvin measures from absolute zero, so only kelvin gives correct results. Add 273.15 to a Celsius value.

With R = 8.314, use pascals for pressure, cubic meters for volume, moles for amount and kelvin for temperature. Convert liters to cubic meters by dividing by 1000.

An ideal gas is a model in which particles take up no space and do not attract each other. Real gases behave almost ideally at ordinary pressures and temperatures.

At very high pressure or very low temperature, when particles are close together and interactions matter. Then a real-gas equation such as van der Waals is more accurate.

Boyle, Charles and Gay-Lussac laws are each special cases of PV = nRT with two quantities held constant. The ideal gas law combines them into one relationship.

No. The calculation runs in your browser and nothing you enter is stored or sent anywhere, unless you choose Save, which keeps the result only on this device.

• Ideal gas law (Wikipedia).
• Gas constant (Wikipedia).
• Ideal gases (Maths Is Fun).